log of the moira

Fractal images are such fun I have included a fractal generation program on this CD so you can make them and see them in 3D animation. Fractinit.exe is a DOS program but it runs just fine on Windows 95. To set up the program, click here. You will (depending on your browser) have an option to either run the compressed file from the CD or to download it to disk. Take your pick. Fractal.exe is just a compressed zip file that self expands the fractal files (1.4 MB) into a folder called Fractal (unless you tell it to put it somewhere else). So feel free to select the option to run it from the CD. If you prefer, you can download the zipped file to your hard drive, find it with your windows explorer, and double click on it. It does the same thing both ways.After Fractal.exe has expanded, go to the Fractal folder using the windows explorer and double click on Fractinit.exe to start the program (you can also start it by using start | run | C:\fractinit.exe). You might want to make a shortcut to the program for your desktop to make it easier to start (do this by right clicking on the file in Windows Explorer and selecting "make shortcut").

Unlike some windows programs that are point and click you will have to read the instructions to learn how to use the program but it is well worth the time. When in doubt, use F1 to pop up a help file. The help files are specific to the part of the program you are in and contain some useful and interesting information about fractals as well as about the program. Once you have a nice fractal on screen, hit the c key twice to see it cycle through the colors. You will never be the same.

The famous Mendelbrot series. Click to zoom in to smaller and smaller sections. You can really play with this in the Fractalinit program I have included on this CD.

Fractals are a new discovery. Without computers nobody would have discovered them and without computers nobody would be looking at them. I have a friend who is a leading statistician of offshore fish populations and he thinks fractals are "computer errors." But there are a host of people who think fractal math is the long awaited pathway to writing formulas for living systems.

$A fractal equation that generates what looks like a fern. Check it out in Fractinit. (t for "type of image" and select "IFS" and then "Fern". If you zoom in on a tiny part of one frond it resolves itself as exactly the same pattern.$ Fractal math resulted in the development of Iterated Function Systems (IFS) that map a region of two dimensional space onto itself using a very small set of functions. The information needed to generate this fern, for example, is in a "seed" file with only 7 numbers in four sets (28 numbers total). Each set has 4 matrix numbers, two vector numbers and a single probability number. A whole forest has been "mapped" onto a file of just 300,000 bytes. In any case, fractals are a very useful metaphor for understanding life.

Individual concepts - either thoughts or creatures - are like part of a fractal curve. One part of the design has an individual shape, with similar ones nearby. Each part is clearly different from its surroundings: different from the larger design it is part of, different from the smaller designs of its fine detail. But it does not exist by itself.

The existence and resolution of the fractal design depends on how many times the computer solves the fractal equation. If the equation is solved only a few thousand times, the design may not be visible at all. Fractals are the surprising patterns that develop by graphing formulas of complex numbers on the two coordinates of your computer screen. The x axis (horizontal) represents real or ordinary numbers. The y axis (vertical) represents imaginary numbers (real numbers multiplied by the square root of minus 1). In a metaphoric sense, this resembles the creation of awareness and its subsequent remaping of probabilities. Biological systems are exposed to real numbers. They "map" these real numbers - expecting that future real numbers will be equal to those already experienced. The mapped numbers held in memory are imaginary, in the sense that they are expectations or representations of real numbers and exist on an imaginary plane. When imaginary numbers and real numbers turn out to be the same (or close enough not to trigger the sensory system), the result is nothing. No reaction, no dot on the display screen. In the Fractal shown to the left, no reaction is represented by black. In the Mandelbrot fractal images no dot is represented by blue. When the expected number and the real one are not the same, the difference generates a point of awareness. The degree of difference between expected and real determines the degree of response. Because the sensors are all in different positions relative to the incoming signals, their combined flow of binary responses impose a second level of iteration in the next highest portion of the parallel computer - for example passing the information to processor clusters in the brain.

The internal computations are all very simple equations done on binary (yes-no) numbers and repeated millions upon millions of times per second. The operation of the retina of the eye is a reasonable example of what might be called parallel processing of fractal images.

Fractal spiral. The spiral is replicated in an infinite depth, the closer you look, the more detail there is.

A sea shell's decision to turn left or right is also based on hundreds or thousands of iterations of incoming sensory information matching real numbers against imaginary remembering. Threading into the equation is the internal state of the sea shell - hungry, frightened, sexually stimulated, searching for darkness or the light. The fractal equation of awareness, the constant remaping of real and imaginary based on surprise, has been solved by the experience of awareness learning new ways to minimize the error of expectations over several billion years.

Any one part of the structure of life on our planet - you or me, for instance - is clearly different from its surroundings and from the larger and smaller designs it is part of. But if we look closely enough at ourselves we find we are comprised of little iterations of becoming and if we look around ourselves we see we belong to larger iterations of becoming. And just like the fractal designs, no matter how closely you look, each pattern is similar, yet different from any other one.